He never sold many records. His biggest hit album, Lick My Decals Off Baby, reached number 20 in the UK in 1970. But in a recording career that lasted from the 1960s until 1982, he succeeded in redefining the parameters of rock music.

His sound shifted over the years, from relatively straightforward blues rock to doomed attempts to court a mainstream audience; but at its height, it reached hitherto-unimaginable heights of avant garde experimentation.

Beefheart's most celebrated album, Trout Mask Replica of 1969, offered a world in which rock music appeared to have spun entirely off its axis.

The singer's earthy holler grounded it in the blues tradition, but the lyrics were wild and surreal. And the music seemed to be from another planet, far beyond even the most acid-fried psychedelic band could muster.

Standard time signatures were disregarded. Instruments – which extended beyond the standard guitar, bass and drums were set up to incorporate bass clarinet and musette – clashed to the point that it frequently sounded like everyone in the Magic Band was playing an entirely different song to everyone else.

The most obvious reference point was free jazz, but the most startling thing about the Magic Band may have been that nobody was improvising: every note had apparently been carefully worked out in advance by Beefheart (he wrote the entire album on piano) and drilled into the band via a regime that former members later protested was little short of tyrannical.

Some 41 years after the album's release, Trout Mask Replica remains the standard by which almost all experimental rock music is judged, its reputation as a fearsomely difficult listen undimmed by the passing of time or its influence.

For every listener who was simply baffled, there was someone whose view of what rock was capable of was changed forever, among them John Peel and Simpsons creator Matt Groening. Their proselytising, and Beefheart's influence (Johnny Rotten was a fan; Tom Waits fell under his spell; The Pixies and Red Hot Chili Peppers all paid tribute) ensured his legacy.

But no one has ever really sounded like the classic Magic Band in full flight: more striking even than their music is the sense that Beefheart achieved something genuinely mysterious, alchemical, inexplicable and unrepeatable.